“Effect of Initial Value on Graph of Exponential Function (C<0)”
Effect of Initial Value on Graph of Exponential Function (C<0)
May 10, 2011
- This site is part of a collection of ready-made interactive classroom activities in mathematics hosted by the MERLOT Math Pedagogic Collection and the Science Education Resource Center (SERC) Pedagogic Service Portal for educators.
The home page at http://serc.carleton.edu/sp/merlot/math/interactive/index.html explains that “making lectures interactive draws students into the lecture by engaging them in working with the material. In an interactive lecture, the lecture is interspersed with short individual, pair, or small-group activities. These activities also provide feedback to the instructor on student understanding.”
A list of the various math examples and interaction types is available at http://serc.carleton.edu/sp/merlot/math/interactive/examples.html Reviews of other specific pages can also be found at MERLOT.
In general the activities include some or all of a five minute “ConcepTest” – where the individual student answers a question and the instructor polls the class, a ten minute Question of the Day – where the student works with a neighbor and records their conclusions in writing, and a fifteen minute Write-Pair-Share activity where students collaborate to refine and expand on the original discussion. The activity also includes a link to an interactive Java applet where the instructor can demonstrate the concepts that the students have been exploring.
This particular page (#48749) is one of four that examine the behavior of the graph of a natural exponential function as the value of the coefficient is changed. Specifically it encourages student exploration of the effect of the coefficient C<0 in f(x)=Ce^(kx).
- Type of Material:
- Tutorial, drill & practice,
- Recommended Uses:
- The main use of the material is as a part of in-class activity.
- Technical Requirements:
- Ability to display Word rtf documents in browser.
Java enabled browser with Flash Player for instructor demonstration portion.
- Identify Major Learning Goals:
- The learning goal of this material is to develop students’ understanding of the effects of coefficients in quadratic functions through exploration and discussion with fellow students.
- Target Student Population:
- Students taking college algebra.
- Prerequisite Knowledge or Skills:
- Some knowledge of college algebra.
- This site contains a ready-to-use in-class activity module that consists of the ConcepTest, Question of the Day, Write-pair-share exercise, and conclusion involving the use of a demonstration applet. Each part is performed by students in succession and is meant to develop student’s understanding of the effect of the initial value, C, on the y-intercept and position of an exponential graph where C<0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). There are three other related modules that explore the graph of a natural exponential function.
- Notice that while there are four exponential function activities, they all use the same interactive demonstration applet and parameters must be adjusted to match the case under investigation.
- An instructor can use this activity “out of the box”. It can be carried out in either a small College Algebra class or a large lecture setting anytime during or after the topic of graphing quadratic functions has been covered.
- The detailed instruction and clear structure of this module makes it very easy to use. Since it is part of a series of activities in similar format the instructor can build familiarity with the nature of such activities throughout the course.
- The display of the Word rtf files in Windows Explorer seemed surprisingly temperamental.
- Creative Commons: